Methods for generating random numbers with a specified probability density function (PDF) are well known. One such method is the Monte Carlo Method. The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer. This can be accomplished, for example, by applying a set of sampled values to a system model implemented on a computer to generate sample results. The method applies to problems with no probabilistic content as well as to those with inherent probabilistic structure.
While the conventional Monte Carlo method is often an acceptable sampling method, it is typically accurate only after it has converged in statistics. This convergence can take a very large number of random samples to provide the desired accuracy. For example, a simulator utilizing the Monte Carlo method may include many loops (for example, “For Loops” would be used in C), nested or otherwise, to generate an accurate statistical sample with multiple random variables. Running such loops with the many iterations can take hours or days, depending on the speed of the computer or processor. Further, the amount of time may increase more than linearly with the number of samples or the number of loops required to achieve convergence. Effective random-number generation is therefore desirable.
Other prior techniques for generating random numbers with a specified PDF utilized “brute force.” For example, a random number sequence uniformly distributed between 0 and 1 was first generated by calling on known system-provided routines. One difficulty with this approach is that it can take a very large amount of data before a sufficiently uniform distribution is realized depending upon application requirements. In cases where non-uniformly distributed random numbers are required, a controlled mapping was typically implemented in a conventional way to “shape” the numbers with the desired PDF. This could be done, for example, by building a lookup table, again with a brute-force mapping. This again can be extremely time consuming.
Thus, it would be desirable to provide a random number generation method that is quicker than prior methods and also reduces the number of samples that must be generated to achieve the desired statistical accuracy.